There is a third way which is put the company into hibernation. I was faced with this with my startup a bit more than 10 years ago now. I ran out of runway so I laid everyone off, paid the bills, and got a job. I then bought out everyone else, worked part time on the business and built it back up over then next few years to the point where I could return full time. I could have started a new business, but I believed that there was a lot of value in the old business [1] which proved to be correct.
1. Some caveats here. Firstly, I did not have many people to buy out and they were willing to sell at a reasonable price. Secondly, my business is in biotech/bioinformatics and we had put a lot of resources into R&D. This R&D had real value that could be used to bring the business back to life.